Theory of time-dependent reactive scattering: cumulative time-evolving differential cross sections and nearside-farside analyses of time-dependent scattering amplitudes for the H + D2 --> HD + D reaction.

Nearside-farside (NF) theory, originally developed in the energy domain for the time-independent description of molecular collisions and chemical reactions, is applied to the plane wave packet (PWP) formulation of time-dependent scattering. The NF theory decomposes the partial wave series representation for the time-dependent PWP scattering amplitude into two time-dependent subamplitudes: one N, the other F. In addition, NF local angular momentum (LAM) theory is applied to the PWP scattering amplitude. The novel concept of a cumulative time-evolving differential cross section is introduced, in which the upper infinite time limit of a half-Fourier transform is replaced by a finite time. In a similar way, a cumulative energy-evolving angular distribution is defined. Application is made to the state-to-state reaction, H + D2(v(i) = 0, j(i) = 0) --> HD(v(f) = 3, j(f) = 0) + D, where v(i), j(i) and v(f), j(f) are vibrational and rotational quantum numbers for the initial and final states, respectively. This reaction exhibits time-direct and time-delayed (by about 25 fs) collision mechanisms. It is shown that the direct-time mechanism is N dominant scattering, whereas the time-delayed mechanism exhibits characteristics of NF interference. The NF and LAM theories provide valuable insights into the time-dependent properties of a reaction, as do snapshots from a movie of the cumulative time-evolving differential cross section.